Several different proposals for the EUTRA synchronization channel (SCH), intended for use in the cell search procedure are proposed in 3rd Generation Partnership Project RAN1 until now. For instance: Motorola, “Cell Search and Initial Acquisition for OFDM Downlink,” R1-051329, Seoul, Korea, Nov. 7-11, 2005 (this paper is called Moto hereinafter).
Compared to the solution existing in the WCDMA standard, Motorola's proposal makes a step forward towards concurrent initial timing acquisition and cell identification. In this way the duration of overall cell search procedure, resulting in timing acquisition and cell identification, is supposed to be shortened.
According to this proposal, the synchronization channel consists of two concatenated identical cell-specific OFDM waveforms, which are preceded by a cyclic prefix of LCP samples. Such SCH is designed to support the initial timing acquisition by using blind differential correlation detection in the receiver, see: T. M. Schmidl and D. C. Cox, “Robust Frequency and Timing Synchronization for OFDM,” IEEE Trans. On Communications, Vol. 45, pp. 1613-1621, December 1997 (this paper is called T. M. Schmidl hereinafter).
The cell identification is performed after the initial timing acquisition, by detecting the cell specific OFDM waveform obtained by modulating the sub-carriers with the elements of a cell-specific Zadoff-Chu sequence of prime length (the Zadoff-Chu sequences are the basis for the generation of a much broader family of so-called GCL sequences, see: B. M. Popovic, “Generalized chirp-like polyphase sequences with optimum correlation properties,” IEEE Trans. On Information Theory, vol. 38, pp. 1406-1409, July 1992. The cell-specific index of the GCL sequence can be detected by using an Inverse Discrete Fourier Transform (IDFT), after the differential encoding of the block of the received signal samples.
Although the above solution for the synchronization channel seems quite promising in terms of reduced overall cell search time, still its timing acquisition is very sensitive to noise/interference due to the broad triangular shape of the differential correlation function.
The SCH signal from Moto consists of a cyclic prefix followed by a synchronization signal s(k), k=0, 1, . . . , N−1, consisting of twice repeated basic cell-specific OFDM waveform W(l), l=0, 1, . . . , N/2−1, where N is the number of samples in the OFDM signal obtained after the IDFT in the transmitter. The timing of the SCH can be detected in the receiver by the following algorithm:                A) Take a block of N received signal samples;        B) Correlate the first N/2 samples of the block with the complex conjugate of the last N/2 samples of the block, and store the resulting differential correlation;        C) Repeat the first two steps for a new block of N samples of the received signal, taken after a delay of one sample compared to the previous block;        D) Find the delay of the block of N samples that result in the maximum correlation magnitude, and select it as the initial timing for OFDM symbol demodulation.        
The differential correlation C(p) of the received signal r(k), k=0, 1, . . . , N−1, can be mathematically represented as
                                          C            ⁡                          (              p              )                                =                                    ∑                              k                =                0                                                              N                  /                  2                                -                1                                      ⁢                                          r                ⁡                                  (                                      p                    +                    k                                    )                                            ·                                                r                  *                                ⁡                                  (                                      p                    +                    k                    +                                          N                      /                      2                                                        )                                                                    ,                            (        1        )            where p denotes the delay of the first sample in the block of N received samples with respect to the true position of the first sample of the synchronization signal, and “*” denotes complex conjugation. If the received signal contains just the repeated waveform W(k) (without the cyclic prefix), then it follows that the differential correlation of the received signal is equal to the differential correlation function CW(p) of the waveform W(k), which exists only for p=0, ±1, ±2, . . . , ±(N/2−1), N is even, and is given by
                                                        C              W                        ⁡                          (              p              )                                =                                                    ∑                                  k                  =                  0                                                                      N                    /                    2                                    -                  1                  -                                                          p                                                                                  ⁢                                                W                  ⁡                                      (                    k                    )                                                  ·                                                      W                    *                                    ⁡                                      (                    k                    )                                                                        =                                          ∑                                  k                  =                  0                                                                      N                    /                    2                                    -                  1                  -                                                          p                                                                                  ⁢                                                                                      W                    ⁡                                          (                      k                      )                                                                                        2                                                    ,                                  ⁢                  p          =          0                ,                  ±          1                ,                  ±          2                ,        …        ⁢                                  ,                  ±                                    (                                                N                  /                  2                                -                1                            )                        .                                              (        2        )            
The differential correlation function of the synchronization signal from Moto, generated by IFFT of N=128 samples, with cyclic prefix of 10 samples, is shown in FIG. 1.
The formula (2) explains the broad triangular-like shape of the differential correlation function in FIG. 1. Small distortions of the triangular shape come from the fluctuations of the signal envelope. Thus, it can be seen from (2) that the differential correlation depends just on the envelope of synchronization signal, so the different synchronization signals with the constant envelope will produce the same differential correlation. The differential correlation function in FIG. 1 reaches a plateau which has a length equal to the length of the cyclic prefix (T. M. Schmidl).
The peak detection of the differential correlation can be done, for example by finding the maximum of the correlation function calculated in a (10 ms) frame of the received samples. However, there might be synchronization signals from multiple cells that can be received concurrently in the user equipment (UE), and all of them should be detected in the cell search procedure. Consequently, the peak detection of the differential correlation in a frame of received samples is not enough, because it cannot discriminate the peaks coming from the different cells.
Instead, or additionally, some kind of threshold-based selection has to be applied. For example, the magnitude of each differential correlation value can be compared with an adaptive threshold proportional to the energy of the signal in the correlation window of N/2 samples used to calculate the observed correlation value, so all the correlation values larger than a certain percentage of the signal energy in the corresponding correlation window will be selected for further processing by peak detection to find the accurate time of arrival of each synchronization signal.
The comparison with the above adaptive threshold is equivalent to comparing the normalized differential correlation as defined in T. M. Schmidl, eq. (8) (normalized with the received energy in the second half-symbol) with a fixed threshold between 0 and 1. As the timing acquisition performances are basically determined by the properties of differential correlation, we shall not discuss further normalization with the signal energy.
An impulse-like differential correlation function is obtained by the OFDM synchronization signal proposed in B. Park et al, “A Novel Timing Estimation Method for OFDM Systems”, IEEE Communications Letters, Vol. 7, No. 5, pp. 239-241, May 2003 (this paper is called B. Park hereinafter), eq. (10) ass(k)=[W(k)Z(k)W*(k)Z*(k)]  (3)where the waveform W(k) of length N/4 samples is generated by IFFT of a pseudo-noise sequence, while the waveform Z(k) is designed to be symmetric with W(k). The synchronization signal (3) is detected by a modified differential correlation, defined as (B. Park)
                              D          ⁡                      (            p            )                          =                              ∑                          k              =              0                                                      N                /                2                            -              1                                ⁢                                    r              ⁡                              (                                  p                  -                  k                                )                                      ·                                          r                ⁡                                  (                                      p                    +                    k                                    )                                            .                                                          (        4        )            
The signal (3) is explicitly and exclusively defined as an OFDM signal, to be generated by the IFFT, so the B. Park does not anticipate other types of centrally symmetric synchronization signals, such as spread-spectrum direct sequence signals.
If neglect the complex conjugation in the signal (3), a person skilled in the art can notice that it is basically a repetitive signal, whose basic repeated waveform of length N/2 samples is centrally symmetric. Such a signal has an impulse-like differential correlation function, but its repetitive structure results in high correlation sidelobes, equal always to the quarter of the signal energy, regardless of the properties of the pseudo-noise sequences used to modulate the sub-carriers within the OFDM signal. The high correlation sidelobes can cause an increased probability of false timing acquisition, so it is desirable to reduce them as much as possible.
Besides, the shorter length (N/2) of the basic waveform repeated in the synchronization signal (3) implies a smaller number of different synchronization signals that can be generated. In the application of interest, such as the cell search in a cellular system (which is not considered in B. Park), where the synchronization signals should not just serve for timing acquisition, but also for the information transmission, the smaller number of potential different synchronization signals with low cross-correlation implies a smaller amount information that can be conveyed by the synchronization signal.
Further on, the complex conjugation of the basic repeated waveform in the second half of the signal might complicate the implementation of the signal generator and demodulator, especially if the signal is supposed to be obtained by the IDFT of a complex pseudo-noise sequence.
Also, the synchronization signal (3) consists of two symmetric waveforms, so N/2 is an even number.
In the paper, Zhang et al. “Joint Frame Synchronization and Frequency Offset Estimation OFDM Systems” IEEE Trans. On Broadcasting, vol. 51, no 3, September 2005, is described a joint frame synchronization and carrier frequency offset estimation scheme. The paper seems mainly be concentrating on improving the frequency error estimation; it is not said how the arrival time of the training symbol should exactly be estimated.